1/x-5/3x=5/6

Solution for 1/x-5/3x=5/6 equation:

1/x-5/3x=5/6

We move all terms to the left:

1/x-5/3x-(5/6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-5/3x-(+5/6)=0

We get rid of parentheses

1/x-5/3x-5/6=0

We calculate fractions


(-45x^2)/108x^2+108x/108x^2+(-180x)/108x^2=0

We multiply all the terms by the denominator


(-45x^2)+108x+(-180x)=0

We get rid of parentheses

-45x^2+108x-180x=0

We add all the numbers together, and all the variables

-45x^2-72x=0

a = -45; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-45)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-45}=\frac{144}{-90}
=-1+3/5
$